{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra/","md":"https://postcutoff.com/e/2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra","date":"2026-11-03","date_precision":"day","short_title":"FPRAS for mixed volumes, ideas from GPT-6 Astra","deck":null,"takeaway":null,"category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2611.01368: An FPRAS for Mixed Volumes (Chen, Liu)","url":"https://arxiv.org/abs/2611.01368","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-11-03","updated":"2026-11-03","orgs":["OpenAI"],"title":"First FPRAS for mixed volumes of convex bodies, disproving a 2009 conjecture of Gurvits; main ideas 'generated entirely by GPT 6 Astra' (Chen, Liu)","summary":"Xiaoyu Chen and Kuikui Liu (arXiv 2611.01368, 3 Nov 2026) give the first fully polynomial-time randomized approximation scheme for the mixed volume of n compact convex sets in R^n given by weak membership oracles, which they say disproves a long-standing conjecture of Gurvits (2009). Their disclosure: \"The main ideas were generated entirely by GPT 6 Astra\"; the paper is a human-written exposition.","key_facts":["Claim: first FPRAS for mixed volumes of arbitrary compact convex sets given by weak membership oracles; 'This disproves a longstanding conjecture of Gurvits [Gur09a, Section 4, item 2]'","AI disclosure (verbatim): 'The main ideas were generated entirely by GPT 6 Astra. The purpose of this paper is to provide a human-written exposition of the algorithm.'","Running time: GPT-6 Astra estimated about n^900 ε^-220 · poly(L); the authors say they have not verified it and 'do not claim it as a proved bound'","Verification status: unrefereed preprint, rewritten and checked by the authors; no formalization"],"key_numbers":[],"tags":["math","computer-science","convex-geometry","approximation-algorithms","gpt-6-astra","arxiv"],"science":{"field":"computer-science","subfield":"approximation algorithms / convex geometry","problem":"Gurvits's conjecture (2009) that mixed volumes admit no FPRAS in the oracle model","result":"FPRAS for mixed volumes of n convex bodies in R^n","open_since":"2009","ai_system":["GPT-6 Astra"],"human_role":"AI-originated: main ideas from GPT-6 Astra, humans simplified and wrote the exposition","verification":{"key":"preprint","label":"Preprint only","text":"Preprint, author-checked"},"status":"pending","shock":""},"body_md":"## What happened\n\nChen and Liu posted an algorithm that approximates mixed volumes to any relative accuracy in randomized polynomial time. They credit the main ideas entirely to GPT-6 Astra and present the paper as their human-written exposition. The polynomial is very large (an unverified model estimate puts it near n^900).\n\n## Why it matters\n\nMixed volumes generalize permanents and volumes; Gurvits had conjectured that no such scheme exists. The result is theoretical, and refereeing has not started.","disputed":[{"label":"Verification","text":"Preprint, author-checked","sources":[]}],"related":[{"id":"2026-11-03-ai-assisted-results-november-3-listing","url":"https://postcutoff.com/e/2026-11-03-ai-assisted-results-november-3-listing/","date":"2026-11-03","date_precision":"day","short_title":"AI-assisted results, 3 Nov: arXiv of 3 Nov and Hexagon of 2–3 Nov","deck":null,"takeaway":"The 3 Nov sweep listed 376 arXiv papers that mention AI, 124 conjecture papers and 69 uncited Hexagon works. Four results got own entries: Kronheimer–Mrowka's primarily AI-generated proposed proof that the dodecahedron web has instanton homology of dimension 64, a second AI-derived proof of the Alon–Seymour–Thomas separator conjecture (with Lean), Chen–Liu's FPRAS for mixed volumes (ideas 'generated entirely by GPT 6 Astra'), and the convergence of three proofs that RM(1,9) has covering radius 242.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":13,"official":13,"filed":"2026-11-03","updated":"2026-11-03","orgs":["OpenAI","Anthropic","Google","various researchers"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-03","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-03","run":null,"sources_read":null,"updated":"2026-11-03","human_review":null,"version":{"date":"2026-11-03"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":187,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":126,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":217,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":156,"in_training_data":false}],"short_url":"https://postcutoff.com/s/fpras-mixed-volumes-ideas"}